Question: $A$ $B$ $C$ If: $ BC = 5x + 4$, $ AC = 48$, and $ AB = 3x + 4$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {3x + 4} + {5x + 4} = {48}$ Combine like terms: $ 8x + 8 = {48}$ Subtract $8$ from both sides: $ 8x = 40$ Divide both sides by $8$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $BC$ $ BC = 5({5}) + 4$ Simplify: $ {BC = 25 + 4}$ Simplify to find ${BC}$ : $ {BC = 29}$